How to calculate probability in a normal distribution given mean & standard deviation?

There's one in scipy.stats:

>>> import scipy.stats
>>> scipy.stats.norm(0, 1)
<scipy.stats.distributions.rv_frozen object at 0x928352c>
>>> scipy.stats.norm(0, 1).pdf(0)
0.3989422804014327
>>> scipy.stats.norm(0, 1).cdf(0)
0.5
>>> scipy.stats.norm(100, 12)
<scipy.stats.distributions.rv_frozen object at 0x928352c>
>>> scipy.stats.norm(100, 12).pdf(98)
0.032786643008494994
>>> scipy.stats.norm(100, 12).cdf(98)
0.43381616738909634
>>> scipy.stats.norm(100, 12).cdf(100)
0.5

[One thing to beware of -- just a tip -- is that the parameter passing is a little broad. Because of the way the code is set up, if you accidentally write scipy.stats.norm(mean=100, std=12) instead of scipy.stats.norm(100, 12) or scipy.stats.norm(loc=100, scale=12), then it'll accept it, but silently discard those extra keyword arguments and give you the default (0,1).]

Scipy.stats is a great module. Just to offer another approach, you can calculate it directly using

import math
def normpdf(x, mean, sd):
    var = float(sd)**2
    denom = (2*math.pi*var)**.5
    num = math.exp(-(float(x)-float(mean))**2/(2*var))
    return num/denom

This uses the formula found here: http://en.wikipedia.org/wiki/Normal_distribution#Probability_density_function

to test:

>>> normpdf(7,5,5)  
0.07365402806066466
>>> norm(5,5).pdf(7)
0.073654028060664664

Here is more info. First you are dealing with a frozen distribution (frozen in this case means its parameters are set to specific values). To create a frozen distribution:

import scipy.stats
scipy.stats.norm(loc=100, scale=12)
#where loc is the mean and scale is the std dev
#if you wish to pull out a random number from your distribution
scipy.stats.norm.rvs(loc=100, scale=12)

#To find the probability that the variable has a value LESS than or equal
#let's say 113, you'd use CDF cumulative Density Function
scipy.stats.norm.cdf(113,100,12)
Output: 0.86066975255037792
#or 86.07% probability

#To find the probability that the variable has a value GREATER than or
#equal to let's say 125, you'd use SF Survival Function 
scipy.stats.norm.sf(125,100,12)
Output: 0.018610425189886332
#or 1.86%

#To find the variate for which the probability is given, let's say the 
#value which needed to provide a 98% probability, you'd use the 
#PPF Percent Point Function
scipy.stats.norm.ppf(.98,100,12)
Output: 124.64498692758187